Very Short Answer on Mathematical Reasoning Class 11 OP Malhotra Exe-27H ISC Maths Solutions Ch-27. In this article you would learn to solve hard questions easily on Mathematical Reasoning. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11.
Mathematical Reasoning Class 11 OP Malhotra Very Short Answer ISC Maths Solutions Ch-27
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 11th |
| Chapter-27 | Mathematical Reasoning |
| Writer | OP Malhotra |
| Exe-27(H) | Very Short Answer Type Questions. |
Very Short Answer on Mathematical Reasoning
OP Malhotra ISC Class 11 Maths Solutions
Que-1: The negation of the statement, ‘Jaipur is the capital of Rajasthan’ is ……..
Sol: The negation of a statement means denying it. So, we simply add “not” to the statement.
Therefore, the negation is: Jaipur is not the capital of Rajasthan.
Que-2: Write the converse of the statement, ‘If x is a prime number, then x is odd’.
Sol: Converse means interchanging hypothesis and conclusion.
Original: If p → q (x is prime → x is odd)
Converse: If q → p
Hence, If x is odd, then x is a prime number.
Que-3: Write the contrapositive of the statement, ‘If the two lines are parallel, then they do not intersect in the same plane.’
Sol: Contrapositive of p → q is ~q → ~p.
Here, p = lines are parallel, q = they do not intersect.
So, contrapositive is: If two lines intersect, then they are not parallel.
Que-4: Write the inverse of the statement, ‘If the weather is clear, then we will go for an outing.’
Sol: Inverse of p → q is ~p → ~q.
So, If the weather is not clear, then we will not go for an outing.
Que-5: The contrapositive statement of the proposition p ⇒ ~q is ……..
Sol: Contrapositive of p → ~q is q → ~p.
Hence, the answer is: If q then not p.
Que-6: Negation of p ∨ q is ……..
Sol: By De Morgan’s Law:
~(p ∨ q) = (~p ∧ ~q)
So, negation is: p and q both are false.
Que-7: Contrapositive of (p ∨ q) ⇒ r is ……..
Sol: Contrapositive of A → B is ~B → ~A
So, ~(r) → ~(p ∨ q)
Using De Morgan’s law:
~r → (~p ∧ ~q)
Que-8: Negation of ~ (p ∧ q) is ……..
Sol: Double negation rule:
~[~(p ∧ q)] = (p ∧ q)
Hence, answer is p ∧ q.
Que-9: Negation of ~ [p ∨ (~ q)] is ……..
Sol: Remove outer negation:
~[~(p ∨ ~q)] = (p ∨ ~q)
Que-10: Converse of the contrapositive of p ⇒ q is ……..
Sol: Contrapositive of p → q is ~q → ~p
Converse of that is: ~p → ~q
Que-11: Write the converse of the inverse of p ⇒ q ……..
Sol: Inverse of p → q is ~p → ~q
Converse of that is: ~q → ~p
Que-12: Assign a truth value to ~ p ∨ q if p is false and q is false ……..
Sol: Given p = False, q = False
~p = True
So, ~p ∨ q = True ∨ False = True
Que-13: Assign a truth value to p ∧ ~ q if both p and q are true.
Sol: Given p = True, q = True
~q = False
So, p ∧ ~q = True ∧ False = False
Que-14: Write negation of the compound proposition p ∨ (~ p ∨ q).
Sol: First simplify inside:
p ∨ (~p ∨ q) = (p ∨ ~p ∨ q)
Since p ∨ ~p = True
Expression becomes True ∨ q = True
Negation of True is False.
Que-15: Form the biconditional statement p ⇔ q if
p = A triangle is an equilateral triangle
q = All three sides of a triangle are equal.
Sol: Biconditional means “if and only if”.
So, the statement becomes:
A triangle is an equilateral triangle if and only if all three sides of the triangle are equal.
–: End Mathematical Reasoning Class 11 OP Malhotra Exe-27H ISC Maths Ch-27 Solutions :–
Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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